MathDB

Perpendicular lines plus two circles

Source:

February 25, 2006

geometrygeometric transformationreflectioncircumcircletrigonometrygeometry proposed

Problem Statement

Point

B

is a midpoint of

C

. Circle

o_1

which passes through

A

and

C

intersect circle

o_2

which passes through

B

and

C

in two different points

C

and

D

. Point

P

is a midpoint of arc

AD

of circle

PQ \perp CD

which doesn't contain

C

. Point

Q

is a midpoint of arc

BD

of circle

o_2

which doesn't contain

C

. Prove that

PQ \perp CD

.

Back to Problems View on AoPS